By taking advantage of the natural stability of the high-energy resummation, recently discovered in the context of heavy-flavor studies, we investigate the inclusive hadroproduction of a neutral heavy-light, hidden-flavored tetraquark (Xcuc¯u¯ or Xbsb¯s¯ state), in association with a heavy (single c- or b-flavored) hadron or a light jet at the (HL-)LHC. We make use of the JETHAD multi-modular working package to provide predictions for rapidity, azimuthal-angle and transverse-momentum distributions calculated via the hybrid high-energy and collinear factorization, where the Balitsky–Fadin–Kuraev–Lipatov resummation of energy logarithms is supplemented by collinear parton densities and fragmentation functions. We rely upon the single-parton fragmentation mechanism, valid in the large transverse-momentum regime, to describe the tetraquark production. Our study represents a first attempt at bridging the gap between all-order calculations of high-energy QCD and the exotics.