\[\large \lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{e^{\frac{k}{n}}+e^{-\frac{k}{n}}}{n\sqrt{11-e^{\frac{2k}{n}}-e^{-\frac{2k}{n}}}} = \sin^{-1}{\left(\frac{e^{a}-e^{-a}}{b}\right)}\]

If \(a\) and \(b\) above are positive integers, find \(a+b\).

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