If you'd rather just spend $40-$60, try this:
If your strips are common anode (the vast majority are), products like this are easy and fast ways to do what you want. YES, you can absolutely do the same thing with power MOSFETs, and I have. This is just the type of device I personally go to when I want to do it all quickly.
A google search for RGB LED amplifier will show you thousands of alternatives.
Seller Ray Wu on aliexpress.com sells inexpensive units that are good quality.