A mini fridge wouldn't even be close to being enough, they're not very powerful at all. They can drop the temp inside as much as 50 degrees going full blast, but an 11x11x8 room is over 500 times that size, so you'd get maybe one or two tenths of a degree drop. Even a full size fridge would probably only drop two or so degrees. You need an AC unit, you can get them new at the end of summer for under $100, or used on CL for under $100 now. I have a tiny little 5K BTU unit I got from Home Depot for $80, it draws <500w at full blast. I'm glad I did because it's just about getting hot enough to need it.
Another thing is to run the 12 on cycle at night, I run mine at 8pm to 8am, so even tho it gets 80 degrees in the day, I still haven't needed the AC yet. Plus you don't need a heater at night (if your area gets cold). So far with no heat or cooling, my room is 65-75 during the day (lights off), 75-82 at night (lights on). If I ran 12 on during the day I'd need to heat at night, and cool in the day, if would just be $ down the drain...
Another idea is if you have a basement or crawl space under the house where it's cool during the day, draw that air into the grow room.
Good luck with it!