One, (20 points) Solve the equation:
$$
(12 x+5)^{2}(6 x-1)(x+1)=\frac{55}{2} \text {. }
$$
One, transforming the original equation, we get
$$
(12 x+5)^{2}(12 x-2)(12 x+12)=660 \text {. }
$$

Let $12 x+5=t$, then $t^{2}(t-7)(t+7)=660$, which is $t^{4}-49 t^{2}=660$.
Solving this, we get $t^{2}=60$ or $t^{2}=-11$ (discard).
Thus, we have $t= \pm 2 \sqrt{15}$, which means $12 x+5= \pm 2 \sqrt{15}$.
Therefore, the roots of the original equation are $x_{1,2}=\frac{-5 \pm 2 \sqrt{15}}{12}$.