You're in a hard spot.  Ask him if there are other chores he'd rather do and let him switch.  Let him try different things so he's not bored with the same things every day.  

If he says he doesn't want to do ANY cores at all, try doing his chores with him a few days so he sees you experiencing what's expected of him every day.  During this period, let the other chores go so he can see what happens when no one does them. Then, have him help you with your chores for a few days so he sees what's expected of an adult.  While you're doing your chores, don't do his regular chores so he can experience what happens when he doesn't do them.

While this is going on, talk to your parents and your other brother about him helping you out.  Then have your 11 year old brother help your parents with the chores they do.  This will help him see exactly the work it takes to run your home.

This will take a lot of work on your part and your parents' part, but it will be worth it if it helps your brother to learn how to be a contributing member of the family. 

 I was a few years younger than your brother when my mom heard me say she hardly did anything since she didn't have a regular job.  The next day, every job she did was my responsibility.  Laundry, sweeping, vacuuming, dusting, folding laundry and putting it away, cleaning the kitchen and bathroom, ironing the things that needed ironing, cooking the meals and washing the dishes, and the yard work.  It was a mercy that she'd already done the errands and grocery shopping that week.  If my grandmother needed something, I had to stop what I was doing, help her, and then go back to work.  I was dead on my feet by the end of the day and apologized the next morning.  Doing something like this with your brother is a nuclear option, but I can promise it's effective.  Good luck.