Let $X$ be a point inside convex quadrilateral $ABCD$ such that $\angle AXB + \angle CXD = 180^{\circ}$. Given $AX = 14$, $BX = 11$, $CX = 5$, $DX = 10$, and $AB = CD$, find the sum of the areas of $\triangle AXB$ and $\triangle CXD$.

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