Skunking, at least what I read in brewing papers, is caused by light reacting with the iso alpha acids and rearranging them into less bitter, more off flavored compounds. Any light can do this, but lower wavelengths (especially UV) have higher energy. If the beer is warm, or worse hot, these reactions can occur faster.
If you're using amber bottles, kegs, and buckets, you're largely fine. If you're using a carboy, you should wrap it in a towel or blanket, or just keep lights off of it. Minimize any light source and you'll be fine.
Lastly, LED bulbs emit typically a very small range of wavelengths, but are very intense light especially right next to the bulb. I am not a physics nut, but i believe this is the inverse square law for light. The father away the light source, the less intense the light is. So, If you leave the LEDs on and right next to your beer in a carboy, hell ya it'll skunk. But if you're only using the LEDs as a light source for your brew room to check on the beer/brew and it's ceiling height you're fine.
Sorry, long answer for that but, Cheers!