I used a $5 Y Splitter cable to split my connection but had to use one of these hum eliminators. I'm told it's because the power from the amp throws everything off. Anyway, that box thing solved it. Lucky for me I already had two extra cables lying around.
Update: I bought the Hum Destroyer box and it works! The noise is completely gone. It does lower the volume on both split outputs, but not enough to be a problem. I did an experiment in Reaper and measured a 10 dB difference in the sound meter there.
For the record, my working setup is:
(/u/ZagatoZee /u/prudensg pinging in case you're interested)