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We present the analysis of SN 2020wnt, an unusual hydrogen-poor super-luminous supernova (SLSN-I), at a redshift of 0.032. The light curves of SN 2020wnt are characterised by an early bump lasting $\sim5$ days, followed by a bright main peak. The SN reaches a peak absolute magnitude of M$_{r}^{max}=-20.52\pm0.03$ mag at $\sim77.5$ days from explosion. This magnitude is at the lower end of the luminosity distribution of SLSNe-I, but the rise-time is one of the longest reported to date. Unlike other SLSNe-I, the spectra of SN 2020wnt do not show O II, but strong lines of C II and Si II are detected. Spectroscopically, SN 2020wnt resembles the Type Ic SN 2007gr, but its evolution is significantly slower. Comparing the bolometric light curve to hydrodynamical models, we find that SN 2020wnt luminosity can be explained by radioactive powering. The progenitor of SN 2020wnt is likely a massive and extended star with a pre-SN mass of 80 M$_\odot$ and a pre-SN radius of 15 R$_\odot$ that experiences a very energetic explosion of $45\times10^{51}$ erg, producing 4 M$_\odot$ of $^{56}$Ni. In this framework, the first peak results from a post-shock cooling phase for an extended progenitor, and the luminous main peak is due to a large nickel production. These characteristics are compatible with the pair-instability SN scenario. We note, however, that a significant contribution of interaction with circumstellar material cannot be ruled out.