Density of rational points on elliptic K3 surfaces

Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K^{\mathrm{\prime }}\mathrm{/}K$ such that the set of $K^{\mathrm{\prime }}$-rational points is Zariski dense in $X$.