Context. The stellar [α/Fe] abundance is sometimes used as a proxy for stellar age, following standard chemical evolution models for the Galaxy, as seen by different observational results. Aim. In this work, we aim to show that the open cluster NGC 6705/M 11 has a significant α-enhancement [α/Fe] > 0.1 dex, despite its young age ( 300 Myr), challenging the current paradigm. Methods: We used high resolution (R > 65 000) high signal-to-noise ( 70) spectra of eight red clump stars, acquired within the OCCASO survey. We determined very accurate chemical abundances of several α elements, using an equivalent width methodology (Si, Ca and Ti), and spectral synthesis fits (Mg and O). Results: We obtain [Si/Fe] = 0.13 ± 0.05, [Mg/Fe] = 0.14 ± 0.07, [O/Fe] = 0.17 ± 0.07, [Ca/Fe] = 0.06 ± 0.05, and [Ti/Fe] = 0.03 ± 0.03. Our results place these clusters within the group of young [α/Fe]-enhanced field stars recently found by several authors in the literature. The ages of our stars have an uncertainty of around 50 Myr, much more precise than for field stars. By integrating the cluster's orbit in several non-axisymmetric Galactic potentials, we establish the M 11's most likely birth radius as lying between 6.8-7.5 kpc from the Galactic centre, not far from its current position. Conclusions: With the robust open cluster age scale, our results prove that a moderate [α/Fe]-enhancement is no guarantee for a star to be old, and that not all α-enhanced stars can be explained with an evolved blue straggler scenario. Based on our orbit calculations, we further argue against a Galactic bar origin of M 11. Full Table 2 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/610/A66