STEP 1:
Given : $y = x^3-11x+5$
Differentiate w.r.t $x$ we get,
$\frac{dy}{dx} = 3x^2-11 ------(1)$
The equation of the given tangent is $y = x-11$
STEP 2:
Hence the slope of the tangent is 1
Now Equating this slope to equ (1)
$\begin{align*} 3x^2 -11 & = 1 \\ 3x^2 & = 12 \\ x^2 & = 4 \\ x & = \pm 2 \end{align*}$
STEP 3:
When $x = 2, y = -9$
When $x = -2, y = -13$
Hence the point is $(2, -9)$