Freddy, the king of flavortext, has an infinite chest of coins. For each number \( p \) in the interval \([0, 1]\), Freddy has a coin that has a probability \( p \) of coming up heads. Jenny the Joyous pulls out a random coin from the chest and flips it 10 times, and it comes up heads every time. She then flips the coin again. If the probability that the coin comes up heads on this 11th flip is \( \frac{p}{q} \) for two integers \( p, q \), find \( p + q \).

Let's think step by step and output the final answer within \boxed{}.
user