Your answer is still correct. It is just that their final answer is simpler.
Your solution \(\displaystyle x=\frac{13\pi}{12} + n\pi\) generates the same set of solutions as the simpler solution given.
For your solution,
when \(\displaystyle n=-1\), \(\displaystyle x=\frac{\pi}{12}\),
when \(\displaystyle n=0\), \(\displaystyle x=\frac{13\pi}{12}\),
when \(\displaystyle n=1\), \(\displaystyle x=\frac{25\pi}{12}\), etc.
For the simpler solution,
when \(\displaystyle n=-1\), \(\displaystyle x=\frac{-11\pi}{12}\),
when \(\displaystyle n=0\), \(\displaystyle x=\frac{\pi}{12}\),
when \(\displaystyle n=1\), \(\displaystyle x=\frac{13\pi}{12}\), etc.