Dimension of the quotient ring of a Noetherian local ring by a principal ideal

Question

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $x\in \mathfrak{m}$. Then it is known that $\dim R/xR \geq \dim R-1$: The dimension modulo a principal ideal in a Noetherian local ring. If we add the additional assumptions on $x$ that $x\notin \mathfrak{m}^2$ and $x$ is not a zerodivisor in $R$, then is it true that the equality $\dim R/xR =\dim R-1$ holds?