On November 13, 2017 I accidentally sent 10 ETH to my ETC wallet this is a common mistake.
That is not a common mistake. Every exchange advice you to send right coins to the right wallet and also warns you the coins will be lost forever if you do. Now, I'm not technically aware what happens when you send a coin to a wrong address but do you think it's recoverable? What are you expecting the support to do? Do they have a way of getting those ETH back?
They can get it back if they want but why would they when they can just keep all 10 ETH