Get your truck weighed and find out the individual f/r axle weights and that will tell you how much of that #6400 GVWR you have left.
If by what you ask about "tow safely" that you want to stay UNDER your trucks ratings, that's gonna be hard to do with a #6500 DRY weight trailer. There are more ratings than just the "tow rating".. ;)
Your actual HITCH ratings does not mean what your truck is rated to haul either.. That sounds like a pretty stout hitch, so that's not going to be your limiting factor.
I towed a #5000 GVWR TT that put my old 97 F150 over it's GVWR by a bit and it was only #150 less than yours.
Good luck!
Mitch