Let \( z \) be a complex number such that \( z^5 = 1 \) and \( z \neq 1 \). Determine the value of the sum
\[
\frac{z}{z-1} + \frac{z^2}{z^2-1} + \frac{z^3}{z^3-1} + \frac{z^4}{z^4-1}.
\] Let's think step by step and output the final answer within \boxed{}.
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