Another Non-Homogenous Diophantine Equation

\[\large 8x^3 - 4 = y(6x-y^2)\]

Find all integer solutions to the above expression. If these solutions can be written as \((x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\), write your answer as

\[n+\displaystyle \sum_{i=1}^n (x_i+y_i).\]

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