Isaac repeatedly flips a fair coin. Whenever a particular face appears for the $2n+1$th time, for any nonnegative integer $n$, he earns a point. The expected number of flips it takes for Isaac to get $10$ points is $\frac{a}{b}$ for coprime positive integers $a$ and $b$. Find $a + b$.

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