2012 AMC 8 Problems/Problem 11

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The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, are all equal. What is the value of $x$?

$\textbf{(A)}\hspace{.05in}5\qquad\textbf{(B)}\hspace{.05in}6\qquad\textbf{(C)}\hspace{.05in}7\qquad\textbf{(D)}\hspace{.05in}11\qquad\textbf{(E)}\hspace{.05in}12$