AoPS Wiki:Problem of the Day/September 16, 2011

When the equation $13^{3x}+13^x=10$ is solved for $x$ , the result is $x=\log_{a}b$ , where $a$ and $b$ are positive integers and $a$ is not a multiple perfect power other than $1$ . Find $(a+b)(a^2-ab+b^2)$ .