  We provide a covariant framework to study singularity-free
Lema\^itre-Tolman-Bondi spacetimes with effective corrections motivated by loop
quantum gravity. We show that, as in general relativity, physically reasonable
energy distributions lead to a contraction of the dust shells. However,
quantum-gravity effects eventually stop the collapse, the dust smoothly bounces
back, and no gravitational singularity is generated. This model is constructed
by deforming the Hamiltonian constraint of general relativity with the
condition that the hypersurface deformation algebra is closed. In addition,
under the gauge transformations generated by the deformed constraints, the
structure function of the algebra changes adequately, so that it can be
interpreted as the inverse spatial metric. Therefore, the model is completely
covariant in the sense that gauge transformations in phase space simply
correspond to coordinate changes in spacetime. However, in the construction of
the metric, we point out a specific freedom of considering a conformal factor,
which we use to obtain a family of singularity-free spacetimes associated to
the modified model.
