As stated on the edit on my question the problem was that CMD from nginx:1.11 was only starting the nginx process. A work around is to place the following command on my Dockerfile
CMD service cron start && nginx -g 'daemon off;'
This will start nginx as nginx:1.11 starts it and well as start the cron service.
The Dockerfile would look something like:
FROM nginx:1.11
# Remove sym links from nginx image
RUN rm /var/log/nginx/access.log
RUN rm /var/log/nginx/error.log
# Install logrotate
RUN apt-get update && apt-get -y install logrotate
# Copy MyApp nginx config
COPY config/nginx.conf /etc/nginx/nginx.conf
#Copy logrotate nginx configuration
COPY config/logrotate.d/nginx /etc/logrotate.d/
# Start nginx and cron as a service
CMD service cron start && nginx -g 'daemon off;'