#MATL, 20 bytes

tVtnw48-PZ}t0<?x_]vs

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Explanation

        % Implicitly grab the input
tV      % Duplicate the input and convert to a string
tn      % Duplicate and find the length of this string
w       % Flip the top two stack elements to get us the string again
48-     % Subtract 48 (ASCII 'O'). Yields a negative number for a negative sign
        % and digits otherwise
P       % Flip the resulting array
Z}      % Break the array up so each element is pushed to the stack
t0<?    % If the first character was a negative sign
  x_    % Pop the negative sign off the stack and negate the first digit
]       % End of if
vs      % Vertically concatenate and sum all stack contents
        % Implicitly display the result

MATL, 20 bytes

tVtnw48-PZ}t0<?x_]vs

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Explanation

        % Implicitly grab the input
tV      % Duplicate the input and convert to a string
tn      % Duplicate and find the length of this string
w       % Flip the top two stack elements to get us the string again
48-     % Subtract 48 (ASCII 'O'). Yields a negative number for a negative sign
        % and digits otherwise
P       % Flip the resulting array
Z}      % Break the array up so each element is pushed to the stack
t0<?    % If the first character was a negative sign
  x_    % Pop the negative sign off the stack and negate the first digit
]       % End of if
vs      % Vertically concatenate and sum all stack contents
        % Implicitly display the result

#MATL, 20 bytes

tVtnw48-PZ}t0<?x_]vs

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#MATL, 20 bytes

tVtnw48-PZ}t0<?x_]vs

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Explanation

        % Implicitly grab the input
tV      % Duplicate the input and convert to a string
tn      % Duplicate and find the length of this string
w       % Flip the top two stack elements to get us the string again
48-     % Subtract 48 (ASCII 'O'). Yields a negative number for a negative sign
        % and digits otherwise
P       % Flip the resulting array
Z}      % Break the array up so each element is pushed to the stack
t0<?    % If the first character was a negative sign
  x_    % Pop the negative sign off the stack and negate the first digit
]       % End of if
vs      % Vertically concatenate and sum all stack contents
        % Implicitly display the result

#MATL, 18 bytes

ZSG|V!UZ}bb*GVnGvs

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#MATL, 20 bytes

tVtnw48-PZ}t0<?x_]vs

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All test cases