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)=2016. Then y can be written in simplest form as \frac{p}{q}. Find p+q. ( \mathbb{R} \backslash\{-1,1\} refers to the set of all real numbers excluding -1 and 1.)