Solution: Since $\gcd (33, 15) = 3$ divides $12$, we can reduce the given equation dividing by $3$. The reduced equation will be \[ 11x \equiv 5\ (\mathrm{mod}\ 4 ) \implies 3x \equiv 1\ (\mathrm{mod}\ 4 ). \] We need to find $x$ such that $4$ divides $3x - 1$. It is clear that $x = 3$ is a solution. Now all solutions will be \[ \left\{ 4n + 3 \mid n \in \mathbb{Z} \right\} . \]