1. The equation
$$
\sqrt[3]{(x+1)(x-4)}+\sqrt[3]{(x+2)(5-x)}=6
$$

has ( ) real solutions.
(A) 0
(B) 1
(C) 2
(D) More than 2
- 1.A.

Let $a=\sqrt[3]{(x+1)(x-4)}$,
$$
b=\sqrt[3]{(x+2)(5-x)} \text {. }
$$

Then $a+b=6, a^{3}+b^{3}=6$.
Thus, $a^{2}+b^{2}-a b=1$. Therefore, $a b=\frac{35}{3}$.
Hence, $a, b$ are the two real roots of the equation $t^{2}-6 t+\frac{35}{3}=0$. However, $\Delta=-\frac{32}{3}<0$, no real solutions.