Suppose \(m\) and \(n\) are real numbers such that the roots of the equation \(2x^2-mx+8=0\) are \(\alpha\) and \(\beta\) while the roots of the equation \(5x^2-10x+5n=0\) are \(\dfrac{1}{\alpha}\) and \(\dfrac{1}{\beta}\).

Find the value of \(mn\).

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