Each of X₁, X₂ and X₃ represents a nonzero digit of the 3-digit base M positive integer X₁X₂X₃; where X₁, X₂ and X₃ are not necessarily distinct.

Determine the possible positive integer values of M, with 7 ≤ M ≤ 206, such that this equation has at least one valid solution.

X₁^X₂ + X₂^X₃ + X₃^X₁ = X₁X₂X₃ ± 6

Note: X₁X₂X₃ denotes the concatenation of the three digits.