Example 6 In the donation activity of a school to the "Hope Project", the total donation amount of $m$ male students and 11 female students in Class A is equal to the total donation amount of 9 male students and $n$ female students in Class B, which is $mn + 9m + 11n + 145$ yuan. It is known that each person's donation amount is the same, and it is an integer number of yuan. Find the donation amount per person.
Notice,
$$
\begin{array}{l}
m n+9 m+11 n+145 \\
=(m+11)(n+9)+46 .
\end{array}
$$

From the problem, we know that $m+11$ and $n+9$ are both divisors of $m n+9 m+11 n+145$. Since each person's donation amount is the same, therefore,
$$
m+11=n+9 \text {, }
$$

and $m+11$ and $n+9$ are both divisors of 46.
Given that $m, n$ are non-negative integers, we have
$$
\begin{array}{l}
m+11 \geqslant 11, n+9 \geqslant 9 . \\
\text { Also, } 46=1 \times 46=2 \times 23, \text { so } \\
m+11=n+9=46
\end{array}
$$

or $m+11=n+9=23$.
When $m+11=46$, the donation amount per person is $(m+11)+1=47$ (yuan);
When $m+11=23$, the donation amount per person is
$$
(m+11)+2=25 \text { (yuan). }
$$

In summary, the donation amount per person is 47 yuan or 25 yuan.