  We explore the ultrafast reflectivity response from photo-generated coupled
phonon-surface Dirac plasmons in Sb$_2$Te$_3$ topological insulators several
quintuple layers thick. The transient coherent phonon spectra obtained at
different time frames exhibit a Fano-like asymmetric line shape of the
$A^2_{1g}$ mode, which is attributed to quantum interference between
continuum-like coherent Dirac-plasmons and phonons. By analyzing the
time-dependent asymmetric line shape using the two-temperature model (TTM), it
was determined that a Fano-like resonance persisted up to $\approx$1 ps after
photo-excitation with a relaxation profile dominated by Gaussian decay at
$\leq$200 fs. The asymmetry parameter could be well described by the TTM for
$\geq$200 fs, therefore suggesting the coherence time of the Dirac plasmon is
$\approx$200 fs.
