  We study a specific model of anisotropic strange stars in the modified
$f\left(R,\mathcal{T}\right)$-type gravity by deriving solutions to the
modified Einstein field equations representing a spherically symmetric
anisotropic stellar object. We take a standard assumption that
$f(R,\mathcal{T})=R+2\chi\mathcal{T}$, where $R$ is Ricci scalar, $\mathcal{T}$
is the trace of the energy-momentum tensor of matter, and $\chi$ is a coupling
constant. To obtain our solution to the modified Einstein equations, we
successfully apply the `embedding class 1' techniques. We also consider the
case when the strange quark matter (SQM) distribution is governed by the
simplified MIT bag model equation of state given by
$p_r=\frac{1}{3}\left(\rho-4B\right)$, where $B$ is bag constant. We calculate
the radius of the strange star candidates by directly solving the modified TOV
equation with the observed values of the mass and some parametric values of $B$
and $\chi$. The physical acceptability of our solutions is verified by
performing several physical tests. Interestingly, besides the SQM, another type
of matter distribution originates due to the effect of coupling between the
matter and curvature terms in the $f\left(R,\mathcal{T}\right)$ gravity theory.
Our study shows that with decreasing the value of $\chi$, the stellar systems
under investigations become gradually massive and larger in size, turning them
into less dense compact objects. It also reveals that for $\chi<0$ the
$f\left(R,\mathcal{T}\right)$ gravity emerges as a suitable theory for
explaining the observed massive stellar objects like massive pulsars,
super-Chandrasekhar stars and magnetars, etc., which remain obscure in the
standard framework of General Relativity (GR).
