The given equation is equivalent to $(6x+7)^2(6x+8)(6x+6)=72$. Let $a=(6x+7)^2$ and $b=(6x+8)(6x+6)$. Then we have $a+(-b)=1$ and $a\cdot(-b)=-72$. Therefore $a$ and $-b$ are the two roots of $$t^2-t-72=0 \implies t_{1,2}=-8, 9$$ Hence, we find $(a, b)=(-8, -9)$ or $(a, b) = (9, 8)$. Because $a=(6x+7)^2\ge 0$, the only possibility is $(a, b)=(9, 8)$, or $$ \left\{ \begin{array}{ccc} (6x+7)^2 &=& 9\\ (6x+8)(6x+6)&=& 8 \end{array} \right. \implies x_{1,2} = -\frac{2}{3}, -\frac{5}{3} $$