Conservation laws are deeply related to any symmetry present in a physical system . Analogously to electrons in atoms exhibiting spin symmetries , it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t = 1/2 (ref.  ). Every nuclear state is thus characterized by a total isobaric spin T and a projection T -two quantities that are largely conserved in nuclear reactions and decays . A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states , including their ground state, labelled by their total angular momentum J and parity π. Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a J  = 5/2 spin assignment is needed to explain the proton-emission pattern observed from the T = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its J   = 1/2 mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei.