Crazy solve

Suppose the integral solutions of the equation : \(x^{3}+10x-1=y^{3}+6y^{2}\) are

\((x_{1},y_{1}),\ldots,(x_{n},y_{n})\).

Find the value of \((x_{1}+y_{1})+\ldots+(x_{n}+y_{n})\).

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