I Love 315 to \infty

x2(y3+z3)=315(xyz+7)x^2\big(y^3+z^3\big)=315(xyz+7)

Let (x1,y1,z1),(x2,y2,z2),,(xn,yn,zn)(x_1, y_1, z_1), (x_2, y_2, z_2), \ldots , (x_n, y_n, z_n) be all of the solutions to the equation above, where x,y,zx, y, z are positive integers. Find k=1n(xk+yk+zk)\displaystyle \sum_{k=1}^{n} (x_k+y_k+z_k) .

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