To find the points of intersection, set the equations equal: \(3x^2 - 4x + 4 = mx + m - 1\).

Rearrange to form a quadratic equation: \(3x^2 - (4 + m)x + (5 - m) = 0\).

For two distinct points of intersection, the discriminant \(b^2 - 4ac\) must be greater than zero.

Here, \(a = 3\), \(b = -(4 + m)\), and \(c = 5 - m\).

Calculate the discriminant: \((4 + m)^2 - 4 imes 3 imes (5 - m)\).

Simplify: \((4 + m)^2 - 12(5 - m) = m^2 + 20m - 44\).

Set the discriminant greater than zero: \(m^2 + 20m - 44 > 0\).

Factorize: \((m + 22)(m - 2) > 0\).

Using the sign chart method, the solution is \(m > 2\) and \(m < -22\).