We obtain the hydrodynamic limit of symmetric long-jumps exclusion in $\mathbb{Z}^{d}$ (for $d≥1$), where the jump rate is inversely proportional to a power of the jump's length with exponent $\gamma+1$, where $\gamma≥2$. Moreover, movements between $\mathbb{Z}^{d-1} \times \mathbb{Z}_{-}^{*}$ and $\mathbb{Z}^{d-1} \times \mathbb{N}$ are slowed down by a factor $\alpha n^{-\beta}$ (with $α>0$ and $β≥0$). In the hydrodynamic limit we obtain the heat equation in $\mathbb{R}^{d}$ without boundary conditions or with Neumann boundary conditions, depending on the values of $β$ and $γ$. The (rather restrictive) condition in previous works (for $d=1$) about the initial distribution satisfying an entropy bound with respect to a Bernoulli product measure with constant parameter is weakened or completely dropped.