Reciprocal Squares of Smooth Numbers

Let $S$ be the set of integers greater than $1$ that are not divisible by any prime numbers greater than $5$. That is, $$S=\{2,3,4,5,6,8,9,10,12,15,16,18,20,\ldots\}$$There are relatively prime positive integers $m$ and $n$ such that $$\frac{m}{n}=\sum_{k\in S}\frac{1}{k^2}=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{8^2}+\cdots.$$ Find $m+n$.