Comment on "A new exactly solvable quantum model in $N$ dimensions" [Phys. Lett. A 375(2011)1431, arXiv:1007.1335]

We pinpoint that the work about “a new exactly solvable quantum model in $N$ dimensions” by Ballesteros et al. [Phys. Lett. A {\bf 375} (2011) 1431, arXiv:1007.1335] is not a new exactly solvable quantum model since the flaw of the position-dependent mass Hamiltonian proposed by them makes it less valuable in physics.