#### Answer

The solutions are $x=\left\{1, 2, 3\right\}$.

#### Work Step by Step

To solve the given equation graphically, perform the following steps:
(1) Graph the function $y=x^3-6x^2+11x-6$ using a graphing utility. Refer to the image below for the graph.
(2) Identify the point/s where the graph touch/cross the x-axis. These are the points where the value of $x^3-6x^2+11x-6$ is zero.
The x-coordinates of these points are the solutions to the given equation.
Notice that the graph crosses the x-axis at $(1, 0)$, $(2, 0)$, and $(3, 0)$.
This means that the solutions to the given equation are $1, 2, $ and $3$.
Thus, the solutions are $x=\left\{1, 2, 3\right\}$.