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QUICK ANSWER
"Cuento" is a form of "cuento", a noun which is often translated as "story". "El mes que viene" is a phrase which is often translated as "next month". Learn more about the difference between "el mes que viene" and "cuento" below.
el mes que viene(
ehl
mehs
keh
byeh
-
neh
)A phrase is a group of words commonly used together (e.g., once upon a time).
1. (general)
b. the coming month
Mi horóscopo dice que encontraré trabajo durante el mes que viene.My horoscope says I will find a job during the coming month.
el cuento(
kwehn
-
toh
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
1. (narrative)
a. story
Te voy a contar un cuento sobre un burro y una serpiente.I'm going to tell you a story about a donkey and a snake.
c. short story
Encontrarás el libro en la sección de cuentos de la biblioteca.You will find the book in the short story section of the library.