Diameter for 60W (5V, 12A) - cable
First you need to double the cable length. A 6.5 foot run is 13 feet to and from. Next you need the max power being delivered. You know it's 12 amps on a single wire. At that point you would use a cable run calculator. I used http://www.powerstream.com/Wire_Size.htm you play around with the numbers until something is acceptable. 

At 6V DC and 12 Amps, you would need 14 AWG cable to be under a 0.5V Voltage droop on the load. That's fine for APA102 style leds.

For Data, since the refresh rate is likely just a few hundred kHz, a coax rg59 or a cat 5 Ethernet cable would be fine.  But since the APA102 needs Data In, Clock In, and ground, go with the cat 5.

Keep in mind that there may be interference from running the power cable parallel to the data cables on your run.