There exist a series such that :\[a_n=\frac{\sqrt{2n+1}-\sqrt{2n-1}}{\sqrt{(2n+1)(2n-1)}}\]Find the sum of first $60$ terms of this series. If the sum can be represented by $ \frac{a}{b}$ where $a$, $b$ are coprime. Find the value of $(b-a)$. Note that: $a_n$ is the general term of the series.