Will my Lenovo W510 WiFi work with a 2.4:5Ghz Netgear N600 WNDR3400 dual-band home broadband router?

Question

My first post ever ... so please be gentle with me.
BACKGROUND:
1. I'm considering a new router to replace my Linksys WRT54G.
2. The Netgear N600 WNDR3400 dual-band home broadband router has a simultaneous 2.4Ghz & 5Ghz AP capability.
3. While I know my Lenovo W510 WiFi works fine at 2.4 Ghz (802.11G), my question is:
QUESTION:
Q: Will my Lenovo W510 laptop wireless card connect at 5Ghz?
NOTES:
Note: The OS is Centos 6.3 Linux (x86_64).
Note: I'm not sure how to tell you WHICH wireless card I have, so I googled and tried this command:
$ /sbin/lspci -knn | grep -i network
WHICH REPORTED:
00:19.0 Ethernet controller [0200]: Intel Corporation 82577LM Gigabit Network Connection [8086:10ea] (rev 06)
03:00.0 Network controller [0280]: Intel Corporation Centrino Ultimate-N 6300 [8086:4238] (rev 35)
$ /sbin/lspci -nn -s 03:00.0
WHICH REPORTED:
03:00.0 Network controller [0280]: Intel Corporation Centrino Ultimate-N 6300 [8086:4238] (rev 35)
$ /sbin/lspci -vv -s 03:00.0
WHICH REPORTED:
03:00.0 Network controller: Intel Corporation Centrino Ultimate-N 6300 (rev 35)
    Subsystem: Intel Corporation Centrino Ultimate-N 6300 3x3 AGN
    Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR+ FastB2B- DisINTx-
    Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
    Latency: 0, Cache Line Size: 64 bytes
    Interrupt: pin A routed to IRQ 32
    Region 0: Memory at f2000000 (64-bit, non-prefetchable) [size=8K]
    Capabilities: <access denied>
    Kernel driver in use: iwlwifi
    Kernel modules: iwlwifi
$ /sbin/modinfo iwlwifi
WHICH REPORTED (edited):
filename:       /lib/modules/2.6.32-279.5.1.el6.x86_64/kernel/driv​ers/net/wireless/iwlwifi/iwlwifi.ko
alias:          iwlagn
description:    Intel(R) Wireless WiFi Link AGN driver for Linux
... stuff ...
parm:           11n_disable:disable 11n functionality (int)
parm:           5ghz_disable:disable 5GHz band (default: 0 [enabled]) (bool)
... stuff ...

Answer 1

As an update, I bought the WNDR3400v2 router and am supremely disappointed with its lack of power - but - the Lenovo W510 DOES work perfectly fine connecting to both the 2.4Ghz and 5Ghz radios.
The problem is the signal strength only twenty feet away up one floor is dismal (as compared to what it was with the ancient Linksys WRT54G for example).
What bothers me is that Netgear goes to great lengths to hide the power output of the radio so I 'suspect' that it is anemic and I don't (yet anyway) suspect the radio on the W510 laptop. Netgear support would only tell me the EIRP at 2.4GHz is 20dBm, and at 5GHz it's double that. So I can only assume the power output from that. If I assume a 5dBi antenna gain for both frequencies, that results in a power output guesstimate of 15dBm (32mW) at 2.4GHz and double that at, i.e., 18dBm or 64mW, at 5GHz.
The other side of the equation, of course, is the power & gain of the W510 radio & antenna.
Do we have specs for the W510 power output & antenna gain (e.g., a typical laptop is about 50mW (roughly 15 to 18 dBm)  pushed into an antenna with a gain of about 1/2 dBi to about 1 dBi at best, regardless of what the specification sheet intimates)?