Well I have looked and can't find the power supply (PSU). First off the 550 ti uses a 400w min PSU and you have to have a 6 pin connecter comming from the PSU to plug on to the card as well.
If you have the normal size PC and not the slimline version and your PSU is good then yes you could up grade to the 550 ti. Now the 550 ti uses 116w from the 12v rail.
So you would have open your case up and look on the PSU for the numbers, something like this 3.3w + 18amp 5w + 20amps 12v + 10 amps or higher.
Also your CPU is not that good and might have a what everybody is calling bottlenecking. The biggest card would be the AMD 6770 before you start bottlenecking. It also requires a 450w PSU.
The HD 6750 is a 450w PSU. The 6670 is a 400w PSU and you don't need a 6 pin connecter for that card. I hope this helps