  In a coalescence plus independent fragmentation approach we calculate the
$p_T$ spectra of the main hadrons: $\pi, K, p, \bar p, \Lambda, \phi$ in a wide
range of transverse momentum from low $p_T$ up to about 10 GeV. The approach in
its main features was developed several years ago at RHIC energy. Augmenting
the model with the inclusion of some more main resonance decays, we show that
the approach correctly predicts the evolution of the $p_T$ spectra from RHIC to
LHC energy and in particular the baryon-to-meson ratios $p/\pi,\bar
p/\pi,\Lambda/K$ that reach a value of the order of unit at $p_T \sim 3\, \rm
GeV$. This is achieved without any change of the coalescence parameters. The
more recent availability of experimental data up to $p_T \sim 10\rm\, GeV$ for
$\Lambda$ spectrum as well as for $p/\pi$ and $\Lambda/K$ shows some lack of
yield in a limited $p_T$ range around 6 GeV. This indicates that the baryons
$p_T$ spectra from AKK fragmentation functions are too flat at $p_T\lesssim 8
\,\rm GeV$. We also show that in a coalescence plus fragmentation approach one
predicts a nearly $p_T$ independent $p/\phi$ ratio up to $p_T \sim 4 \rm\, GeV$
followed by a significant decrease at higher $p_T$. Such a behavior is driven
by a similar radial flow effect at $p_T< 2 \,\rm GeV$ and the dominance of
fragmentation for $\phi$ at larger $p_T$.
