The GT-10 has very rudimentary amp control ability. With the correct cable, it could switch between two channels of the 6505+ (not the third channel or effects loop). Some of the earlier GT series had problems with ground loops when using the Amp Control jack - I'm not sure if they've corrected it in the GT-10.
To get full control of the 6505+ from the GT-10, a Mini Amp Gizmo (plus 6505+ interface cable) would do the job. The Amp Gizmo would also do the job, but wouldn't really get you anything else for the extra cost (unless you're planning on using more than one amp at a time).