A great effort has been devoted to connect the slowing down of the dynamics of glass-forming liquids to the growing of either static or dynamic length scales. In particular the static picture of low temperature liquids provided by the Random First Order theory defines a growing static length scale assuming the existence of a surface tension between amorphous structures. \par We developed two methods to reveal and measure the amorphous surface tension in a soft sphere glass-former. The results we obtained are perfectly compatible with the Random First Order theory in presence of a distribution of surface tension. Furthermore the heterogeneous dynamics itself seems to be the expression of a phase-separated regime controlled by the amorphous surface tension.