LED Driver and PWM

Okay, I got my shift registers and am able to turn many LEDs on and off. Your multiple LED circuit lets me light those LEDs at the same intensity (using PWM pins without the shift register). But I need to combine these. I need many LEDS at many different intensities. Here is exactly what I'm doing:

I'll have 5 sets of LEDS. Each set will be made up of 4 Red, 4 Green, and 4 Blue. For one set of LEDs, I might want to set all Greens to 100, Reds to 255, Blues to 100. The next set of LEDs will have different values. This way each set of LEDs can be installed behind a sheet of paper ans something to diffuse the light into one color - thus all colors of the rainbow, hopefully!

Is my original assumption that I need a LED driver correct? Or is there some way to force the shift register to output a PWM so I can have one pin of the shift register control one color of a set? I've tried making the shift register do this with delays - lighting a red for 10ms, then off, then on for 10ms hoping it would be the same as sending a PWM of 30 to the Red.

Thanks! Sorry I'm so confused. I'm still learning.

Branton