Natural Pays 6:5 - Should I Double Down?

Hello Everybody - I have not seen any math on this and am wondering if anyone has devoted any time to this subject. With the proliferation of 6:5 payouts on a Natural, is there any advantage to doubling down on this 11? As a card counter, it seems there may be a count where this becomes profitable, but does it ever overcome the shorted payout?
Many thanks in advance - RC