How much can I hang from a blinds bracket?
Wow, I would be very hesitant to employ that idea. That sounds like a catastrophe waiting to happen. And if your landlord has to come into your apartment and sees what you did s/he might not be happy with your idea at all. 

Is it stipulated in your lease that you can't hang anything on the walls? I've lived in many areas and in several states. And from my experience, as long as I fill in any holes and leave the apartment the way it was when I first moved I have never had any problems. 

Mirrors are heavy glass. I would want to support eleven pounds on the wall with something that goes into a stud. But if the drywall is in excellent shape this should suffice:

Picture hanger

That has a 75lb weight load capacity. It's just one small nail head that could be filled with toothpaste once you remove it and move away. 

I would be surprised if you can't hang anything on your walls. I don't think I would rent an apartment that prohibited me from hanging a small mirror on the wall. Perhaps call your landlord and ask. Maybe s/he will feel better doing her/himself. Good luck!