"My mom likes mango."
Translation:אמא שלי אוהבת מנגו.
You'd use את only before a definite object.
In "My mum likes mango", the object and is "mango". "Mango" is indefinite, so there's no את:
אמא שלי אוהבת מנגו
But if you were to say "My mum likes the mango", the object and is now "the mango". "The mango" is definite, so now you have to use את:
אמא שלי אוהבת את המנגו
Is that clear? If you're not sure what definite and indefinite mean, let me know and I'll try and explain some more.