Circumcircle Of A Triangle In A Coordinate Plane

Geometry Level 3

Let $A(-8, 4)$ and $B(6, 6)$ be points in the coordinate plane. Point $C(0, k)$ is such that the circumcircle of $\triangle ABC$ has equation $x^2+y^2+2x-10y-24=0$. Determine the sum of all possible values of $k$.

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