Algebra Level 5

Suppose $$a$$ and $$b$$ are two positive real numbers such that the roots of the equation $$x^{3} - ax + b = 0$$ are all real. Let $$t$$ be a root of the equation with minimal absolute value. If maximum value of $$t$$ is of the form $$\dfrac{mb}{na}$$. Find $$m + n$$.

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