I have a cube rendered on the screen which represents a car (or similar).

Using Projection/Model matrices and Glm I am able to move it back and fourth along the axes and rotate it left or right.

I'm having trouble with the vector mathematics to make the cube move forwards no matter which direction it's current orientation is. (ie. if I would like, if it's rotated right 30degrees, when it's move forwards, it travels along the 30degree angle on a new axes).

I hope I've explained that correctly.

This is what I've managed to do so far in terms of using glm to move the cube:

glm::vec3 vel; //velocity vector

void renderMovingCube(){

    glUseProgram(movingCubeShader.handle());
    GLuint matrixLoc4MovingCube = glGetUniformLocation(movingCubeShader.handle(), "ProjectionMatrix");  
    glUniformMatrix4fv(matrixLoc4MovingCube, 1, GL_FALSE, &ProjectionMatrix[0][0]);

        glm::mat4 viewMatrixMovingCube;
        viewMatrixMovingCube = glm::lookAt(camOrigin, camLookingAt, camNormalXYZ);

        vel.x = cos(rotX); vel.y=sin(rotX);
        vel*=moveCube;

        //move cube 
        ModelViewMatrix = glm::translate(viewMatrixMovingCube,globalPos*vel);

        //bring ground and cube to bottom of screen
        ModelViewMatrix = glm::translate(ModelViewMatrix,  glm::vec3(0,-48,0));
        ModelViewMatrix = glm::rotate(ModelViewMatrix, rotX, glm::vec3(0,1,0));     //manually turn

        glUniformMatrix4fv(glGetUniformLocation(movingCubeShader.handle(), "ModelViewMatrix"), 1, GL_FALSE, &ModelViewMatrix[0][0]); //pass matrix to shader
    movingCube.render();        //draw
    glUseProgram(0);
}

keyboard input:

void keyboard()
{
    char BACKWARD  = keys['S']; char FORWARD   = keys['W'];
    char ROT_LEFT  = keys['A']; char ROT_RIGHT = keys['D'];

    if (FORWARD) //W - move forwards
    {
        globalPos += vel;
        //globalPos.z -= moveCube;
        BACKWARD = false;  
    }
    if (BACKWARD)//S - move backwards
    {
        globalPos.z += moveCube;
        FORWARD = false;  
    }
    if (ROT_LEFT)//A - turn left
    {
        rotX +=0.01f;
        ROT_LEFT = false;  
    }
    if (ROT_RIGHT)//D - turn right
    {
        rotX -=0.01f;
        ROT_RIGHT = false; 
    }

Where am I going wrong with my vectors? I would like change the direction of the cube (which it does) but then move forwards in that direction.