Consider the matrix $$J_{6} = \begin{bmatrix} 0&0 &0 &0 &0 &1 \\ 0& 0& 0& 0& 1&0 \\ 0& 0& 0& 1& 0&0 \\ 0&0 & 1& 0&0 &0 \\0 &1 &0 &0 &0 &0 \\1 &0 &0 &0 & 0& 0\end{bmatrix}$$
which is obtained by reversing the order of the columns of the identity matrix $I_{6}.$ Let $P = I_{6} + \alpha\: J_{6},$ where $\alpha$ is a non-negative real number. The value of $\alpha$ for which $\text{det(P)} = 0$ is _______.
