Sometimes drawing a diagram can help a lot.
You're going to have to sew two pieces of fabric together to get a 72" long rectangle. I'm going to assume that you are not going to try to do any pattern matching with your fabric.
First, you cut 4 lengthwise rectangles as long as you can get, which for you is 6.5" x 60". Assuming that you will lose 1/4" on each side of your seam, you need 4 rectangles that are 6.5" x 12.5", so you can cut one 6.5" x 50" strip and then subcut into the 6.5" x 12.5" rectangles. If it was me doing it, I would cut the strip for the extra rectangles the full length (6.5" x 60") and wait to subcut until you are close to putting on the borders, so that you can adjust the length of those rectangles if you need a little extra length.
Fabric has less stretch along its length than along its width, so cutting your borders lengthwise means the will stretch less and help keep your quilt nice and square.