I have a Panaflo 80x80x25 fan (your typical 80mm size fan) that pushes about 45CFM. It's clearly audible at its highest speeds, but it's a low hum and whoosh, and not a high pitch annoying whine like you usually get from REALLY high RPM fans.
I've had a 6000 RPM fan before. Trust me. You don't want one. I'd stay under 4000 RPM if possible.
With a fan controller, I can turn it down so it fades into the ambient noise, and it still pushes a decent amount of air. But the power is there if I need it.
I've got a pair of them doing exhaust work on an archaic Antec 1080B. They do the job pretty well, and they have a lot more space to suck from than a tiny 360. I bet one of these would do the job just fine and might not force you out of the room.