# Find the sum of all solutions.

Level pending

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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