I can't find a mistake in reasoning : Let $M_1$ NTM (Non Deterministic Turing Machine) that solves $L$ in polynomial-time. So then $x \in L \Leftrightarrow M_1(x) = 1$. Finally our new NTM $M_2$ that solves $\bar{L}$ is inverted $M_1$ : $x \in \bar{L} \Leftrightarrow M_2(x) = 1 \Leftrightarrow M_1(x) = 0$. And since I have NTM $M_2$ that solves $\bar{L}$ then $\bar{L} \in NP \rightarrow coNP \subset NP$. And vice versa $NP \subset coNP$.
May you help me?