Aims: We seek to provide abundances of a large set of light and neutron-capture elements homogeneously analyzed that cover a wide range of metallicity to constrain globular cluster (GC) formation and evolution models. Methods: We analyzed a large sample of 885 GCs giants from the SDSS IV-Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. We used the Cannon results to separate the red giant branch and asymptotic giant branch stars, not only allowing for a refinement of surface gravity from isochrones, but also providing an independent H-band spectroscopic method to distinguish stellar evolutionary status in clusters. We then used the Brussels Automatic Code for Characterizing High accUracy Spectra (BACCHUS) to derive metallicity, microturbulence, macroturbulence, many light-element abundances, and the neutron-capture elements Nd and Ce for the first time from the APOGEE GCs data. Results: Our independent analysis helped us to diagnose issues regarding the standard analysis of the APOGEE DR14 for low-metallicity GC stars. Furthermore, while we confirm most of the known correlations and anticorrelation trends (Na-O, Mg-Al, C-N), we discover that some stars within our most metal-poor clusters show an extreme Mg depletion and some Si enhancement. At the same time, these stars show some relative Al depletion, displaying a turnover in the Mg-Al diagram. These stars suggest that Al has been partially depleted in their progenitors by very hot proton-capture nucleosynthetic processes. Furthermore, we attempted to quantitatively correlate the spread of Al abundances with the global properties of GCs. We find an anticorrelation of the Al spread against clusters metallicity and luminosity, but the data do not allow us to find clear evidence of a dependence of N against metallicity in the more metal-poor clusters. Conclusions: Large and homogeneously analyzed samples from ongoing spectroscopic surveys unveil unseen chemical details for many clusters, including a turnover in the Mg-Al anticorrelation, thus yielding new constrains for GCs formation/evolution models. Full Table 2 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A191