The roots of the equation \(2\sqrt{x} + 2x^{-\frac{1}{2}} = 5\) can be found by solving the quadratic equation \(kx^2 + mx + n = 0\). What are the values of \(k\), \(m\), and \(n\) in the equation? Please provide the sum of \(k\), \(m\), and \(n\).

Let's think step by step and output the final answer within \boxed{}.
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