Previous results in the literature have found the young inner-disc open cluster NGC 6705 to be mildly alpha-enhanced. We examined this possibility via an independent chemical abundance analysis for 11 red-giant members of NGC 6705. The analysis is based on near-infrared APOGEE spectra and relies on LTE calculations using spherical model atmospheres and radiative transfer. We find a mean cluster metallicity of [Fe / H] = +0.13 +/- 0.04, indicating that NGC 6705 is metal-rich, as may be expected for a young inner-disc cluster. The mean alpha-element abundance relative to iron is , which is not at odds with expectations from general Galactic abundance trends. NGC 6705 also provides important probes for studying stellar mixing, given its turn-off mass of M similar to 3.3M(circle dot). Its red giants have low C-12 abundances ([C-12/Fe] = -0.16) and enhanced N-14 abundances ([N-14/Fe] = +0.51), which are key signatures of the first dredge-up on the red giant branch. An additional signature of dredge-up was found in the Na abundances, which are enhanced by [Na/Fe] = +0.29, with a very small non-LTE correction. The O-16 and Al abundances are found to be near-solar. All of the derived mixing-sensitive abundances are in agreement with stellar models of approximately 3.3M(circle dot) evolving along the red giant branch and onto the red clump. As found in young open clusters with similar metallicities, NGC 6705 exhibits a mild excess in the s-process element cerium with [Ce/Fe] = +0.13 +/- 0.07.