Answer
$x=8$
Work Step by Step
Square both sides and put all terms on one side. Divide both sides by $x$. One of the answers does not work.
$\sqrt {6x+1}=x-1$
$(\sqrt {6x+11})^2=(x-1)^2$
$6x+1=x^2-2x+1$
$x^2-8x=0$
$x^2=8x$
$x=0,8$
$\sqrt{6\times0+1}\ne0-1$
$x=8$
