...as it just so happens, I also have a 709 cutter. No complaints, but in hindsight, instead of the medium duty cutter, if I had to do it again I may have gone with the heavy duty version (not sure of the price differential).
It does a fine job of cutting, but I do feel like I am beating the living heck out of it some-times (too many hidden rocks on my property). I guess once I have mowed the entire place for several seasons, I'll have cleaned out the rocks I can and clearly mark those that I can't.
The 5410 handles it no problem, so I am sure either your 5510 or 6310 will as well.