jmc

We can eliminate answer choices $\text{(A)}5$ and $\text{(C)}7$, because of the above statement. Now we need to test the remaining answer choices. Case 1: $x=6$ Mode: $6$ Median: $6$ Mean: $\frac{37}{7}$ Since the mean does not equal the median or mode, $\text{(B)}6$ can also be eliminated. Case 2: $x=11$ Mode: $6$ Median: $6$ Mean: $6$ We are done with this problem, because we have found when $x=11$, the condition is satisfied. Therefore, the answer is $\boxed{11}$.