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Why doesn’t the vacuum energy implied by quantum field theory—through the known Standard Model fields and their radiative corrections—curve spacetime catastrophically, driving either an exponentially rapid expansion or collapse? Supersymmetry is known to ameliorate this long-standing Cosmological Constant Problem, but only down to the scale set by the susy-breaking mass splittings; at least ~TeV for the visible sector. String theory offers new possibilities. I will present an explicit non-supersymmetric string construction in which the open-string (particle physics) contributions to the one-loop vacuum energy exactly cancel between a visible brane sector and a symmetry-enforced hidden mirror sector, whilst the remaining closed-string (gravitational) contributions are suppressed in the size of one or two large extra dimensions (a.k.a. "dark dimensions") and can naturally lie near the observed Dark Energy scale. I'll conclude by discussing the key observational challenges and opportunities of the scenario.