A mere word will reveal the solution

Calculus Level 3

\[\large \displaystyle \int_{{121 \pi} / {6}}^{{61 \pi} / {3}} (\cos x + \sin x) \, dx\]

If the integral above can be expressed as \(\displaystyle \frac{a}{1+\sqrt{b}} \), what is the value of \( a+b\)?

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