Nginx alias configuration for API with Silex - api

Question

I've a problem with my NGinx configuration, I know there is a lot of topics already, but I didn't manage to my working properly...
So I've mydomain.com and mydomain.com/api/, my folders are like:
/var/www/mydomain.com/website/dist and /var/www/mydomain.com/api/public
And at the moment, I've something almost working. But the index.php still get the /api part in my routes.
server {
listen 80;
server_name mydomain.com www.mydomain.com;
index index.php index.html;
location / {
root /var/www/mydomain.com/website/dist;
}
location ~ ^/api(/|$) {
root /var/www/mydomain.com/api/public;
try_files $uri /api/index.php;
location ~ \.php$ {
try_files $uri /index.php =404;
fastcgi_split_path_info ^(.+\.php)(/.+)$;
fastcgi_index index.php;
fastcgi_pass unix:/tmp/php5-fpm.sock;
include fastcgi_params;
fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
fastcgi_param APPLICATION_ENV production;
}
add_header 'Access-Control-Allow-Origin' '*';
add_header 'Access-Control-Allow-Headers' 'X-Requested-With,Content-Type,Authorization';
add_header 'Access-Control-Allow-Methods' 'GET, POST, PUT, DELETE, OPTIONS';
}
access_log /var/logs/nginx/logs/mydomain.com-access.log;
error_log /var/logs/nginx/logs/mydomain.com-error.log;
}
I guess I'm not understanding something with the location or with php-fpm. What did I miss ? What should I do to get this working properly ?
I read too that a try_file is enought for that, than a rewrite rule... I don't know :/
Thank you for your help !