To tackle this problem, we first need to understand and translate the given natural language description into a symbolic representation of an optimization problem. The variables in question are 'grams of protein' (which we'll denote as `x1`) and 'milligrams of vitamin D' (denoted as `x2`). 

The objective function aims to maximize `6.74*x1 + 7.11*x2`.

Given constraints can be summarized into the following inequalities:
- Immune support index: `11*x1 + 1*x2 >= 60` and `11*x1 + 1*x2 <= 87`
- Digestive support index: `12*x1 + 19*x2 >= 18` and `12*x1 + 19*x2 <= 53`
- Energy stability index: `6*x1 + 6*x2 >= 18` and `6*x1 + 6*x2 <= 39`
- Additional constraint: `10*x1 - 3*x2 >= 0`

Now, let's put this into the requested symbolic representation format:
```json
{
    'sym_variables': [('x1', 'grams of protein'), ('x2', 'milligrams of vitamin D')],
    'objective_function': '6.74*x1 + 7.11*x2',
    'constraints': [
        '11*x1 + 1*x2 >= 60',
        '11*x1 + 1*x2 <= 87',
        '12*x1 + 19*x2 >= 18',
        '12*x1 + 19*x2 <= 53',
        '6*x1 + 6*x2 >= 18',
        '6*x1 + 6*x2 <= 39',
        '10*x1 - 3*x2 >= 0'
    ]
}
```

Next, we will translate this problem into Gurobi Python code. Note that Gurobi requires a specific environment setup and the installation of its software and Python interface.

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables (no bounds specified for now)
x1 = m.addVar(name="grams_of_protein", lb=0)  # Assuming non-negativity
x2 = m.addVar(name="milligrams_of_vitamin_D", lb=0)  # Assuming non-negativity

# Objective function: Maximize
m.setObjective(6.74*x1 + 7.11*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(11*x1 + 1*x2 >= 60, "immune_support_min")
m.addConstr(11*x1 + 1*x2 <= 87, "immune_support_max")
m.addConstr(12*x1 + 19*x2 >= 18, "digestive_support_min")
m.addConstr(12*x1 + 19*x2 <= 53, "digestive_support_max")
m.addConstr(6*x1 + 6*x2 >= 18, "energy_stability_min")
m.addConstr(6*x1 + 6*x2 <= 39, "energy_stability_max")
m.addConstr(10*x1 - 3*x2 >= 0, "additional_constraint")

# Solve the model
m.optimize()

if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of protein: {x1.x}")
    print(f"Milligrams of vitamin D: {x2.x}")
else:
    print("No optimal solution found.")
```