#### Answer

$m=\{ -20,2 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|m+9|=11
.$ Do checking of the solution/s.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
m+9=11
\\\\\text{OR}\\\\
m+9=-11
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
m+9=11
\\\\
m=11-9
\\\\
m=2
\\\\\text{OR}\\\\
m+9=-11
\\\\
m=-11-9
\\\\
m=-20
.\end{array}
If $m=2,$ then
\begin{array}{l}\require{cancel}
|m+9|=11?
\\\\
|2+9|=11?
\\\\
|11|=11?
\\\\
11=11
\text{ (TRUE)}
.\end{array}
If $m=-20,$ then
\begin{array}{l}\require{cancel}
|m+9|=11?
\\\\
|-20+9|=11?
\\\\
|-11|=11?
\\\\
11=11
\text{ (TRUE)}
.\end{array}
Hence, $
m=\{ -20,2 \}
.$