Triangle $ABC$ is an isosceles triangle with $\overline{AB}=\overline{BC}$. Point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE}$, and $\overline{CE}$ is $11$ units long. Triangle $ABD$ is congruent to triangle $ECD$. If the length of $\overline{BD}$ is $x$ units, what is the value of $10x$?

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