Good luck expanding!

Find the absolute value of the sum of all integral \(x\) and \(y\) for which the equation

\[x^3+(x+1)^3+(x+2)^3+(x+3)^3+\dots+(x+7)^3=y^3\]

is satisfied. As an explicit example, if the solutions were \((3, 7)\) and \((9, 9)\), you would be asked to find \(3+7+9+9\).

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