How overload C++ functions in Lua using generic function template

Question

I have C++ overloaded functions and want to use it in Lua. I am trying to make a generic C function (called by Lua) to call them depending of arguments. I have little experience in modern C++ and have no ideia if this is really possible.

This is a pseudocode:

void foo(int value){
...
}

void foo(std::string value){
...
}


template<Ret, Func1, Func2, ...>
Ret overload(lua_State *L){
    if (lua_tointeger(L, 1))
        Func1(lua_tointeger(L, 1));

    if (lua_tostring(L, 1))
        Func2(lua_tostring(L, 1));
}

Using LuaBridge to bind:

luabridge::getGlobalNamespace (L)
  .beginNamespace ("test")
    .addFunction ("foo", overload<(void (*)(int))&foo, (void (*)(std::string))&foo>)
  .endNamespace ();

Is this possible? Can anyone help me?