The problem is IMO that NOTHING is really fun if you are depressed (or sleep deprived, for that matter). Sure there is some reciprocity, mundane tasks make you even more depressed. But if you get depression under control, then you will either find a way out of those tasks, or learn to enjoy them.
I don’t think that shitty tasks themselves can cause depression; it’s all about the social context of the work you are doing. Is your boss bullying you, or telling you that you are not important to the organization, or does she try to punish your mistakes? Are you working just to support a study you are not really into, because you think you owe it to your parents? Is there another job you would like better, but you dare not change jobs because you are afraid you won’t earn enough to support yourself? That’s the way to get depressed about the tasks you are doing. Sort out the social context, and you might even realize afterwards that the tasks were not so mundane after all.