**Category:** Algebra  
**Subtype:** Logarithmic Equations  
**Problem Description:** Find the values of the parameter \(m\) such that the equation \(\log_{3}^{2} x - (m+2) \cdot \log_{3} x + 3m - 1 = 0\) has two solutions \(x_{1}\) and \(x_{2}\) where the product \(x_{1} \cdot x_{2} = 27\).