In his paper "Smooth models for elliptic threefolds" (In: The Birational Geometry of Degenerations, Progress in Mathematics, v. 29, Birkhauser, (1983), 85-133), Rick Miranda mentions in the example of section 8 (page 101-102) that it is an unfortunate fact of life that there are no small resolutions for the singularity of the threefold defined by the equation

$$y^2=u^2+v^2+w^3\quad \text{in}\quad \mathbb{C}^4.$$

He said that it is a theorem of Brieskorn but he does not give a reference. Anyone has a reference to this theorem and its proof?

Updated (following some of the answers, the question can be generalized right away):

More generally the same question can be asked for

$$y^2=u^2+v^2+w^{2k+1}\quad \text{in}\quad \mathbb{C}^4, \quad\text{where} \quad k \in \mathbb{N}_0.$$