Define the function $f: \mathbb{R} \backslash\{-1,1\} \rightarrow \mathbb{R}$ to be $$ f(x)=\sum_{a, b=0}^{\infty} \frac{x^{2^{a}} 3^{b}}{1-x^{2^{a+1} 3^{b+1}}} $$ Suppose that $f(y)-f\left(\frac{1}{y}\right)=2021 .$ Then, $y$ can be written in simplest form $\frac{p}{q} .$ Compute $p+q$
