[Solution] The equation of the line symmetric to the line $x-3 y+11=0$ with respect to the $x$-axis is $x+3 y+11=0$, which is $y=-\frac{1}{3} x-\frac{11}{3}$.

Then
Therefore
$$
\begin{array}{c}
m=-\frac{1}{3}, \quad b=-\frac{11}{3} . \\
m+b=-\frac{1}{3}-\frac{11}{3}=-4 .
\end{array}
$$

Hence, the answer is $(C)$.
$25 \cdot 7$ The line $y=m x+b$ is symmetric to the line $x-3 y+11=0$ with respect to the x-axis, then the value of $m+b$ is
(A) -6 .
(B) -5 .
(C) -4 .
(D) -3 .
(E) -2 .
(43rd American High School Mathematics Examination, 1992)