What’s the most straightforward way to ask Mathematica to find all solutions of an equation like

3x + 2y + 4z == 0 (mod 11)

(for instance), where *either* x, y, z can be considered to be integers in the range -5…5,

*or* equivalently they belong to the ring Z/(11Z) of integers modulo 11 ?

(I’ve tried a number of obvious things with no success.)