**Category:** Algebra  
**Subtype:** Polynomial Functions  
**Problem Description:** Determine the range of values for \(m\) such that the equation \(f(x) + m = 0\) has three distinct solutions.  

In this problem, you are given a cubic function \(y = x^3 - x - 1\) and its behavior (increasing/decreasing) based on its derivative. You need to find the values of \(m\) that allow the horizontal line \(y = -m\) to intersect the curve of the function at three different points.