Are you using any kind of accessory that taps into the rear fan header?
When one fan isn't working it's usually because of this and a Transistor has blown. It's fixable, but only if you know how to remove and install that kind of part. The Transistors for the fans are pretty much just big enough to handle the fan it drives, they're not intended to drive anything else at all.
You'll be doing some soldering to get it working again for sure. DO NOT connect both fans up to the one that is still working either (in case you had that idea) that will just add more strain on the working fan's Transistor and cause it to fail prematurely as well.
The Transistor is a BCP51 or ZT751 (either one will work as a replacement) and are SMT. There is one on each side of the boar right at the fans connector. Top one is for the GPU side fan (Q3A2) and the bottom one is for the CPU side fan (Q3M1).
If you're lucky that's all that was toasted and replacing it will get the fan going again. Alternately you can just cut the Red and Brown wires and run them to some 5v or 12v spot on the motherboard and drive the fans that way. This drives the fans faster and moves more air at 12v, but also make a good deal more noise. The fans run at 5v and are thermally controlled an will run up to 12v if the 360 is too hot or if there is a problem somewhere, so running them from an alternate 5v or 12v source will eliminate the thermally controlled function it has.