It's likely that by plugging in the LED device you're connecting the chassis of the audio box to the ground somehow. There are some pretty lengthy papers about this in audio land but basically you want a 'ground loop isolator'.
Think of it like this: You have your audio amplifier with a power supply and then an amp circuit. The amp circuit itself should be "floating in mid air" and never connected to the ground. You might notice the humming effect if you sometimes touch your car stereo with your hand and get a bit of a hum or 'better reception'. High quality receivers go to great lengths to insulate the amp from the ground.
You're then connecting that amp to the speakers, which are mounting in a box, floating in mid air, via the +/- speaker wires, who are also floating entirely in mid air.
If you were to connect the speaker chassis to an earth ground and the amp to an earth ground then their respective distance from each other would result in a humming sound equivalent to 'how out of phase' their respective electromagnetic fields were (because you have basically attempted to use the negative speaker wire as both a ground for power and for audio).
In order to avoid this, you can either 1) Make all your components hover in mid air (very difficult to do.) or 2) Make quite certain that there is no grounding connection that is shared between the speakers and the receiver (still very difficult to do, but slightly more attainable).
First thing to try is hook up all the audio by itself and see if there is any discernable humming. If not, plug in the power cord to your LED system with the ground/neutral connected to a different outlet. If the humming stops, then look for a power outlet based ground loop isolator. If it continues, then you likely have some other low voltage ground wire that is interconnecting the two chassis together and you would have to systematically isolate those from each other. There are available some inexpensive ground loop isolators that help with this issue between components so if it turns out that you have an audio interconnect between your LED system and your AMP that is likely your culprit (and the most logical place to insulate the ground). These would put a transformer in line to interrupt the ground.