It's a qualified YES that you should be able to run FCPX on your MBP.
It's likely a MBP made after early 2011 and it's likely a 2.53GHz Core 2 Duo. Essentially all Unibody 13" MBPs came after mid 2010 with the first being a 2.4GHz box with a NVIDIA GeForce 320M graphics processor that checks out on the link that James tipped you to. That 2010 model will work as yours should.
Buy that FCPX!