Assuming it is solvable, then $x$ must be co-prime to $11$. By Fermat's little theorem, we have $x^{10}\equiv 1\pmod{11}$. However $$1\equiv x^{10}\equiv \left(x^5\right)^2 \equiv 3^2\equiv 9\pmod{11}$$

cannot hold. This is a contradiction. This means this equation has no solution.