  We study the kinetics after a low temperature quench of the one-dimensional
Ising model with long range interactions between spins at distance $r$ decaying
as $r^{-\alpha}$. For $\alpha =0$, i.e. mean field, all spins evolve coherently
quickly driving the system towards a magnetised state. In the weak long range
regime with $\alpha >1$ there is a coarsening behaviour with competing domains
of opposite sign without development of magnetisation. For strong long range,
i.e. $0<\alpha <1$, we show that the system shows both features, with
probability $P_\alpha (N)$ of having the latter one, with the different
limiting behaviours $\lim _{N\to \infty}P_\alpha (N)=0$ (at fixed $\alpha<1$)
and $\lim _{\alpha \to 1}P_\alpha (N)=1$ (at fixed finite $N$). We discuss how
this behaviour is a manifestation of an underlying dynamical scaling symmetry
due to the presence of a single characteristic time $\tau _\alpha (N)\sim
N^\alpha$.
