Short answer No. You have an integrated graphics card. You can pick up a cheap DX11 5770 for around $100 and plug that sucker into your machine, now that will support DX11
This. DX 11 support is mainly from newer Graphics cards. That's an integrated solution, and quite a few generations old, and only supports up to DX9. Also, for true DX 11 support your OS must be more than XP (Vista or 7). However, the DX 6XXX series was notoriously stable compared to it's predecessor, and cheap, giving it a prolonged life-span, particular in the integrated arena.