1. The number of real solutions to the equation $\sqrt{x+19}+\sqrt[3]{x+95}=12$ is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
$-1 . B$.
Let $\sqrt{x+19}=m, \sqrt[3]{x+95}=n$, then $m+n=12$.
$$
\begin{array}{l}
\therefore m=12-n . \\
\text { Also } n^{3}-m^{2}=76 .
\end{array}
$$

Substituting equation (1) into equation (2) and rearranging, we get
$$
\begin{array}{l}
n^{3}-n^{2}+24 n-220=0, \\
(n-5)\left(n^{2}+4 n+44\right)=0 .
\end{array}
$$

Since $n^{2}+4 n+44>0$, it follows that $n=5$.
Thus, $\sqrt[3]{x+95}=5$. Solving for $x$ gives $x=30$.
Upon verification, $x=30$ is the only root of the original equation.