No you're not. And your landlord could probably even charge you rent until May 11th.
In New York, landlords are not required to mitigate damages. This means, they don't have to try and find a tenant right away when you breach your agreement.
No duty to mitigate damages for residential landlords in NYC | Real Estate Weekly
If your landlord moved someone in before May 11th, though, he probably would not be allowed to collect rent from both of you for the same time period.
And as far as how much rent he should deduct, I'm not sure where you are getting 11 days. You said you gave notice on the 11th, but when did you actually vacate?
Either way, you owe rent for every day you were still there, and every day until May 11th or until the day someone else moved in, in my opinion.
Some states also require notice to be given prior to the first of a month, too, and if New York is one of those states, you'd be on the hook for all of May, too.
So, if all he did was keep your April rent, you got a good deal, in my opinion.