Isomers close to doubly magic 78 28Ni50 provide essential information on the shell evolution and shape coexistence near the Z ¼ 28 and N ¼ 50 double shell closure. We report the excitation energy measurement of the 1=2þ isomer in 79 30Zn49 through independent high-precision mass measurements with the JYFLTRAP double Penning trap and with the ISOLTRAP multi-reflection time-of-flight mass spectrometer. We unambiguously place the 1=2þ isomer at 942(10) keV, slightly below the 5=2þ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with discrete nonorthogonal shell-model calculations which are used here for the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other N ¼ 49 isotones. The 1=2þ isomer is interpreted as the bandhead of a low-lying deformed structure akin to a predicted low-lying deformed band in 80Zn, and points to shape coexistence in 79;80Zn similar to the one observed in 78Ni. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart.