The stability or instability of nuclei in the mass region A = 68-82 with 34 Z 40 is studied on the basis of the cluster decay process in these nuclei. The nucleus ⁷⁶Kr is found to be the most stable nucleus in this region, and that, in each case, moving away from the most stable isotope by the addition or subtraction of neutrons, the resulting parent nuclei are found to be highly unstable against all possible (Q > 0) cluster decays. Such an extra stability at Z = 36 and N = 40 points to the possible existence of new shell stablilizing effects at these nucleon numbers, which can be understood as reinforcing of the (deformed) Z = 36 stable shell with the (spherical/deformed) N = 40 stable shell, resulting in a superdeformed ⁷⁶Kr nucleus. The instability with both the addition and subtraction of neutrons is due to major shell closure of the daughter products. In view of the possible consequences of this paper for both nuclear structure and cold fusion studies, further calculations are called for the shell gaps and the possible use of these nuclei as cold reaction partners.