The values of $\alpha$ for which $\begin{vmatrix} 1 & \dfrac{3}{2} & \alpha+\dfrac{3}{2}\\[4pt] 1 & \dfrac{1}{3} & \alpha+\dfrac{1}{3}\\[4pt] 2\alpha+3 & 3\alpha+1 & 0 \end{vmatrix}=0$ lie in the interval: