Problems need HardWork 24

For prime \(x\), let \((x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\) be all the integer solutions of \((x,y) \) such that they satisfy the equation \(x-y^4=4 \). Find the value of \( \displaystyle \sum_{j=1}^n (x_j+ y_j) \).

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