Born in Ciego de Avila, in 2002 she began her dance studies in the Art School "Luis Casas Romero" of the city of Camagüey. Five years later she continued at the Academy of Arts "Vicentina de la Torre" in the same town. During her student years she appeared in two editions of the International Ballet Competition for Students held in Havana, and won gold medals. Upon graduation she joined the Ballet of Camagüey. In this company she achieved the rank of Principal Dancer. Her repertoire consists of the main characters of historical ballets as Grand Pas de Quatre, Swan Lake, La fille mal gardée, Paquita, the pas de trois of The Fairy Dolls, Don Quixote, the second act of the ballet Giselle and The Dying Swan of Michel Fokine. She has danced Cuban choreographer ballets like Vivaldi by Jose Antonio Chavez, Majísimo by Jorge Garcia, Avalanche by Osvaldo Beiro, Forms for concern by Menia Martinez and Nisi Dominus by Jorge Lefebre, including more contemporary works as the Pilgrims duet by Gonzalo Galguera.
In 2015 she became part of Acosta Danza. With this company she has danced Tocororo Suite and Carmen, by Carlos Acosta. With Carlos Acosta as a partner, Laura premiered in Cuba the female lead role of Don Quixote (scenes), in the Acosta version. She has also danced Mil años después, choreography by Saburo Teshigawara; Belles Lettres, by Justin Peck; Rooster, by Christopher Bruce; Paysage soudain, la nuit, by Pontus Lidberg; Imponderable and Alrededor no hay nada, by Goyo Montero; Mundo Interpretado, by Juliano Nunes; Soledad, by Rafael Bonachela; Babbel 2.0, by María Rovira; Soledad, by Rafael Bonachela; Portal, by Juanjo Arqués; Avium, by Ely Regina Hernández; Anadromous and Satori, by Raúl Reinoso; Twelve, by Jorge Crecis; Rodríguez participated in Carlos Acosta’s show “A Classical Farawell” in United Arab Emirates, United Kingdom and Hong Kong, performing the pas de deux Diana and Acteón and the ballet Majísimo with Carlos Acosta; as well as the love duet between Carmen and Escamillo in Carlos Acosta´s version of Carmen. As a member of Acosta Danza she participated in the film Yuli, a film about the life of Carlos Acosta, directed by Icíar Bollaín. In 2021, Laura accompanied Carlos Acosta in the show "On Before", in the United Kingdom.
