\[\large{\dfrac{1}{m-\alpha}+\dfrac{1}{m-\alpha^2}+\cdots+\dfrac{1}{m-\alpha^n}}\]

Let \(P(z)=z^{n+1}-1\) have roots \(1, \alpha, \alpha^2, \ldots, \alpha^n\) where \(\alpha\) is a \((n+1)^\text{th}\) root of unity and \(m\) isn't a \((n+1)^\text{th}\) root of unity.

Find the value of the expression above.

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