There are two values of \(a\) for which the equation \(4x^2 + ax + 8x + 9 = 0\) has only one solution for \(x\). The discriminant of the quadratic equation can be expressed in the form \(m + n = 0\). Please find the sum of these values of \(m\) and \(n\).

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