\[\large \int \frac{dx}{\sqrt{e^{5x}}\cdot \sqrt[4]{(e^{2x} + e^{-2x})^3}} = -\sqrt[p]{q + e^{-rx}} + C\]

Evaluate the integral above and find \(p + q + r\).

**Notation:** \(C\) denotes the constant of integration.

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