Me dijeron que ...
works, but would normally be used if a plural subject exists elsewhere in the sentence, or if one was previously established in the conversation. For example:
¿Qué dijeron los médicos?
Me dijeron que todo resultó bien.
The English phrase 'was told' is in the passive voice. The subject isn't known or isn't really important to convey. In Spanish, 'I was told' is said 'se dijo' or 'se dijeron'. You could throw the indirect object pronoun
me in the middle of each phrase, but that isn't totally necessary. The reflexive looking 'se' can be translated as 'someone,' 'one,' or 'they' in English, to make more sense of the construct. See more information
here.