The given figure does not show an accurate graph for f(x) = -x^3 + x and thus does not seem viable.
Whereas the local minimum for f(x) = -x^3 + x is -2/(3√3) ≈ -0.38, the graph seems to show a local minimum near or at -1.
Also, coordinate plane in the figure is distorted in that the vertical distance between 0 and -1 seems much smaller than the horizontal distance between 0 and -1.
To avoid confusion, I would ignore the problem as written.
I believe that the following revision reflects the intent of the problem.



Given any function f(x):
f(x) + 10 --> the graph shifts UP 10 places
f(x) - 10 --> the graph shifts DOWN 10 places
f(x-10) --> the graph shifts to the RIGHT 10 places
f(x+10) --> the graph shifts to the LEFT 10 places



The red dot on f(x) moves up 1 place and to the left 2 places to become the green dot on g(x).
Since g(x) shifts the graph of f(x) up 1 place, n=1.
Since g(x) shifts the graph of f(x) to the left 2 places, m=2.
Thus:
m+n = 2 + 1 = 3