Quadratic Diophantine Equation

Find the sum of the values of \( a \) for which the equation \( ax^{2} - 4x + 9 = 0 \) has integer roots.

If the sum you found is of the form \( \dfrac{m}{n} \), where \( m\) and \(n \) are coprime natural numbers, submit \( m+n \) as your answer.

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