i think in order to remove the dirt, u can try using the bleach
if the light colour shirt is not white, use 'colour bleach'
otherwise(if colour bleach doesn't work, or the light colour shirt has a label that it is not suitable for bleaching), u can throw it away-_-
actually, to wash the clothes, u should divide them into different colours
u can't wash the clothes with all colours altogether
remember that can avoid from this case