Let $a$ be a non-zero real number, and $b$ and $c$ be real numbers. For the function $f(x) = ax + b$ defined on the set of real numbers and its inverse function $f^{-1}$,
$$\begin{aligned}
& \lim_{x \rightarrow b} \frac{f(x)}{f^{-1}(x)} = c \\
& f(1) = 3
\end{aligned}$$
are given.
Accordingly, what is the sum of the different values that $c$ can take?
A) 6
B) 7
C) 10
D) 11
E) 14