\(pt\Leftrightarrow\sqrt{3x+1}-4+1-\sqrt{6-x}+3x^2-14x-5=0\)
\(\Leftrightarrow\frac{3x+1-16}{\sqrt{3x+1}+4}+\frac{1-\left(6-x\right)}{1+\sqrt{6-x}}+\left(x-5\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left[\frac{3}{\sqrt{3x+1}+4}+\frac{1}{1+\sqrt{6-x}}+3x+1\right]=0\)
\(\Leftrightarrow x=5.\)