issues with ground loop from DAC?

I notice the DAC uses a safety equipment ground..... For a test try a ground cheater on the DAC power cord plug and then check for hum.

Are you using balanced outputs on the DAC? If not that also may help if you can.

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I don't think your problem is because the Rogue is a tube amp (Unless, as Tsugury suggests, you actually have a bad tube). One thing you may want to try, even if it is only temporary, is one of those "cheater" plugs that bypasses the ground pin to see if that may help. Most likely, getting a line conditioner that isolates the components, will fix the issue.

ZD542--thanks--but not a big fan of cheater plugs
I am using An Audience line conditioner