Noisy MOSFET RGB LED driver problem
I've two suggestions for you.

1) Run separate power and earth wires (as thick as possible) between the power supply and each of the LED and servo driver boards so that they don't share any power wiring.

2) Get a couple of large ferrite beads designed for noise suppression and thread each of the supply wires through them, maybe 2 or 3 turns.

If you add your capacitors it would probably be best to add them to the driver board inputs as the PSU output will most likely have built in capacitors already, or at least will be low impedance.