Find the sum of all solutions.

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Let \(5\)-tuples of positive integers \((x^{(1)}_{1},...,x^{(1)}_{5})\),\((x^{(2)}_{1},...,x^{(2)}_{5})\),....,\((x^{(n)}_{1},..,x^{(n)}_{5})\) satisfy the following system of equations:

\(x_{i}+x_{i+1}=x_{i+2}^{3}\) , \(1≤i≤5\) \(x_{6}=x_{1},x_{7}=x_{2}\).

Find \(\sum_{i=1}^{n}(x^{(i)}_{1}+...+x^{(i)}_{5})\)

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