  We construct a minimal dynamical system of mean dimension equal to $1$, which
can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$.
This clarifies a seemingly plausible impression about embedding possibility in
relation to mean dimension. Our result finally leads to a full understanding of
a pair of exact ranges of all the possible values of mean dimension, within
which there will always be a minimal dynamical system that can/cannot be
embedded in the shift action on the Hilbert cube.
