Will my cory cats be okay without food for 11 days?

Eleven days isn't all that long for fish to not be fed, if you have a planted tank. Both for hiding in and chewing on.

If you go with a mechanical fish feeder, test it before you leave. Make sure it is located far enough away from any mists or splashing areas or the food will cake or rot. Remember the water level will drop and splashing may occur in areas it doesn't occur in now.

There are some newer gel vacation feeders that don't change the water chemistry like the plaster of paris types.
Here is one: Tetra Vacation Gel Feeder Block 14 days

http://www.amazon.com/Tetra-Vacatio...=2025&creative=165953&creativeASIN=B000HHQ5GY

I used the Zoo Med 14 day block feeder when I went away for 2.5 weeks and it worked pretty good. I used it in my 10 gallon in conjunction with an auto-feeder (set to once a day feeding). My 10 gallon had about 15 endlers and 4 cories. When I came back there was still a bit of the block leftover but all my fish were well fed and happy (fry everywhere doing well), but it did cause some excess algae growth. In retrospect, I'd rather have used a 7 day block and fast the fish for a week, but the fry probably enjoyed the constant food source the block supplied.

I haven't heard many good things about the Tetra gel blocks, however I've heard that the API 7 day feeder is the best one so far. I'm going on a trip soon as well, and I'll probably try using the API one.

This is where I've found some of these blocks (and other fish accessories) to be pretty cheap, and it has free shipping. Go to "Food & Supplements" and then "Vacation Feeders" and they're all listed there.

If you use the auto-feeder, can you put a little food in for an every other day feeding? Or set it to feed a small fraction of your normal amount? That way they would get a little food, but not enough to make a big mess while you are gone.

I've had green cory's go 2 weeks without food in a lightly planted tank, they'll probobably will be fine.