A unit cube $ABCDEFGH$ (see the figure) is cut by a plane $\text{S}$ that intersects the edges $AB$ and $AD$ at the points $P$ and $Q$ respectively, such that $AP=AQ=x$ ($0<x<1$). Let the common point of the edge $BF$ and $\text{S}$ be $R$. What is the distance $BR$ if $\angle QPR={120}^{\circ }$?