Cyclically 91

Find the sum of integers cc for all triples of integers (a,b,c),(a,b,c), abc,a\leq b \leq c, that satisfy the system of equations {a2bc=91b2ac=91c2ab=91\begin{cases} a^2-bc=91\\ b^2-ac=91\\ c^2-ab=91 \end{cases}

Details and assumptions

If a number cc appears in several different triples (a,b,c),(a,b,c), it must be counted with multiplicity.

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