Points $A(11, 9)$ and $B(2, -3)$ are vertices of $\triangle ABC$ with $AB=AC$. The altitude from $A$ meets the opposite side at $D(-1, 3)$. What are the coordinates of point $C$? Provide your answer as an ordered pair \((m, n)\). Please give the value of m + n.

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