A pure vortex beam carrying m-order orbital angular momentum (OAM) will be deformed when transmitting through a thin slab, and "neighboring" sideband {m + 1} and {m-1} modes will emerge. The emergence of the OAM sideband is accompanied with OAM-dependent Goos-Hänchen (GH) shift. When the energies carried by the {m} mode of the transmitted beam and by the sideband modes are identical, the OAM-dependent shifts reach their upper limits, |m|w0/2(|m| + 1)1/2, where w0 is the incident beam waist. The epsilon-near-zero metamaterial is found to be suitable to achieve the upper-limited OAM-dependent GH shifts. These findings provide a deeper insight into the beam shifts of vortex beams and have potential applications in the optical sensing, detection of OAM, and other OAM-based applications.