Let the line \(\displaystyle \frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4} \) intersect the plane containing the lines \(\displaystyle \frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1} \) and \( 4\alpha x-y+5z-7a=0=2x-5y-z-3,\; a\in \mathbb{R} \) at the point \( P(\alpha,\beta,\gamma) \). Then the value of \( \alpha+\beta+\gamma \) is equals ______.
