A segment through the focus $F$ of a parabola with vertex $V$ is perpendicular to $\overline{FV}$ and intersects the parabola in points $A$ and $B$. Find $\cos\left(\angle AVB\right)$. The original answer is in the form -\frac{k}{m}, where k and m are integers. Please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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