We introduce the perturbative $\hbar$-power series ($\hbar$ - Planck
constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar$-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters
of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS
symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive
terms in $\hbar$-power series can be calculated explicitly if we supplement
the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative
momenta, which together define the canonical tensorial Heisenberg
algebra.