\[ \large \int_0^\infty \dfrac{\cosh(nx)}{\cosh(\pi x) } \, dx \]

For constant \( |n | < \pi \), the value of the integral above is equal to

\[ \dfrac AB \sec \left ( \dfrac{n^C}D \right) \]

where \(A,B,C\) and \(D\) are positive integers with \(A,B\) coprime.

Calculate \(A+B+C+D\).

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