$\begin{array}{l}
y' = 3{x^2} + 2x + m\\
HS\,co\,cuc\,dai,\,cuc\,tieu \Leftrightarrow \Delta ' = 1 - 3m > 0 \Leftrightarrow m < \frac{1}{3}\\
Khi\,do\,hs\,co\,{x_{CT}} = \dfrac{- 1 + \sqrt {1 - 3m} }{3} > 0 \Leftrightarrow \sqrt {1 - 3m} > 1 \Leftrightarrow 1 - 3m > 1 \Leftrightarrow m < 0
\end{array}$