Triangles $ABC$ and $ADE$ have areas $2007$ and $7002$, respectively, with $B = (0,0)$, $C = (223,0)$, $D = (680,380)$, and $E = (689,389)$. Find the sum of all possible x-coordinates of $A$.

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