My age is everywhere

Calculus Level 5

\[ \large \displaystyle\int _{ 0 }^{ \infty }{ \dfrac { 1 }{ 1+{ x }^{ 13 } } \, dx } =\dfrac { a }{ b } \pi \csc { \left( \dfrac { \pi }{ c } \right) } \]

If the equation above holds true for positive integers \(a,b\) and \(c\), with \(a,b\) coprime, find \(a+b+c\).

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