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The mechanisms that maintain turbulence in the interstellar medium (ISM) are still not identified. This work investigates how we can distinguish between two fundamental driving mechanisms: the accumulated effect of stellar feedback versus the energy injection from Galactic scales. We perform a series of numerical simulations describing a stratified star forming ISM subject to self-consistent stellar feedback. Large scale external turbulent driving of various intensities is added to mimic galactic driving mechanisms. We analyse the resulting column density maps with a technique called Multi-scale non-Gaussian segmentation that separates the coherent structures and the Gaussian background. This effectively discriminates between the various simulations and is a promising method to understand the ISM structure. In particular the power spectrum of the coherent structures flattens above 60 pc when turbulence is driven only by stellar feedback. When large-scale driving is applied, the turn-over shifts to larger scales. A systematic comparison with the Large Magellanic Cloud (LMC) is then performed. Only 1 out of 25 regions has a coherent power spectrum which is consistent with the feedback-only simulation. A detailed study of the turn-over scale leads us to conclude that regular stellar feedback is not enough to explain the observed ISM structure on scales larger than 60 pc. Extreme feedback in the form of supergiant shells likely plays an important role but cannot explain all the regions of the LMC. If we assume ISM structure is generated by turbulence, another large scale driving mechanism is needed to explain the entirety of the observations.