Let $k$ and $m$ be real numbers. The functions $f$ and $g$ defined on the set of real numbers are
$$\begin{aligned}
& f(x) = 2x^{3} - 9x^{2} - mx - k \\
& g(x) = x^{3} \cdot f(x)
\end{aligned}$$
The functions $f$ and $g$ have local extrema at $x = -1$.
What is the sum $k + m$?
A) 31
B) 33
C) 35
D) 37
E) 39