AMC 8 2012 Problem 11

The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and $x$ are all equal. What is the value of $x$? $\textbf{(A)}\hspace{.05in}5 \textbf{(B)}\hspace{.05in}6 \textbf{(C)}\hspace{.05in}7 \textbf{(D)}\hspace{.05in}11 \textbf{(E)}\hspace{.05in}12$