  Sextic oscillator in D dimensions is considered as a typical quasi-exactly
solvable (QES) model. Usually, its QES N-plets of bound states have to be
computed using the coupled Magyari's nonlinear algebraic equations. We propose
and describe an alternative linear method which is N-independent and works with
power series in 1/\sqrt(D). Main merit: simultaneous exact solvability (for all
the QES states) in the first two leading orders (the degeneracy is completely
removed, the unperturbed spectrum is equidistant). An additional merit: All the
perturbation corrections are given by explicit matrix formulae in integer
arithmetics (there are no rounding errors).
