Tear the basil,mint and coriander leaves roughly and set aside. Cut the sweet potato in large chunks and cook in simmering water for 15 minutes until tender. Drain and cut into 1 cm cubes.
Scrub the mussels well,pull out hte beards and discard any that don't close when tapped. Heat the oil,water,shallots,garlic and chilli in a heavy lidded pan and bring to the boil.
Add the mussels,cover tightly and leave for a minute or two. Shake the pan,then remove any opened mussels with tongs. Cover again,give the pan a big shake,remove any opened mussels and so on.
Add the sweet potato,fish sauce,sugar and sweet chilli sauce to the broth,stirring. Add the mussels,herbs and lime juice and toss well. Serve with lime wedges and steamed rice.