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I just put the CCM kit on my Tahoe and im running 305/55R20 and I dont rub at all. I had to trim only the black plastic in the fenderwells. There are also a few other guys on this site with that lift and different tire combos. Look through the other forums, there are a bunch of different about your topic.
CCM kit is a 2.5" front spacer and 1" rear spacer. With this kit on my truck, the rear is ~0.25" higher (not noticable). If you carry heavy loads or tow, I would recommend getting a 1.5" rear spacer. In my case I installed Airlift 1000 air bags and have them set at 20 psi when camping.