AHSME 1991 Problem 20

The sum of all real $x$ such that $(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3$ is $\textbf{(A) } \frac32 \textbf{(B) } 2 \textbf{(C) } \frac52 \textbf{(D) } 3 \textbf{(E) } \frac72$