A tunnel is defined by \( y = \sin x + 5 \) revolved around the x-axis within the domain \( x \in [0, 20 \pi ] \). Suddenly, the whole tunnel is filled completely with cement. Magic happens and only the cement cast is left. If \( V \), the volume of the cement cast in cubic units, can be represented in the form \(a \pi^{b} \), where \(a \) and \(b\) are integers, find \(a+b\).

**NB:** Please evaluate the integral by hand, or you'll miss out on the fun!

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